Reference no: EM131036
Q.1 . Evaluate the following indefinite integrals:
![677_Evaluate the indefinite integrals.png](https://www.expertsmind.com/CMSImages/677_Evaluate%20the%20indefinite%20integrals.png)
Q.2. Using the method of integration by parts evaluate the following integral:
![1594_Evaluate the indefinite integrals1.png](https://www.expertsmind.com/CMSImages/1594_Evaluate%20the%20indefinite%20integrals1.png)
Q.3. Evaluate the following integrals:
![1081_Evaluate the indefinite integrals2.png](https://www.expertsmind.com/CMSImages/1081_Evaluate%20the%20indefinite%20integrals2.png)
Q. 4. Evaluate the following integrals:
![1816_Evaluate the indefinite integrals3.png](https://www.expertsmind.com/CMSImages/1816_Evaluate%20the%20indefinite%20integrals3.png)
Q.5. First find the partial fraction composition and then evaluate the following integral:
![2039_Evaluate the indefinite integrals4.png](https://www.expertsmind.com/CMSImages/2039_Evaluate%20the%20indefinite%20integrals4.png)
Q. 6. Find the area of the shaded region by (i) integrating with respect to x and (ii) integrating with respect to y. [10]
![1204_Evaluate the indefinite integrals5.png](https://www.expertsmind.com/CMSImages/1204_Evaluate%20the%20indefinite%20integrals5.png)
Q.7 (i) Sketch the region enclosed by the following curves.
(ii) Find the volume of the solid that results when the region enclosed by the following curves is revolved around the x-axis.
![2157_Evaluate the indefinite integrals6.png](https://www.expertsmind.com/CMSImages/2157_Evaluate%20the%20indefinite%20integrals6.png)
Q.8 Use cylindrical shells method to find the volume of the solid generated when the region enclosed by the following curves is revolved about the y-axis. First sketch the region.
![130_Evaluate the indefinite integrals7.png](https://www.expertsmind.com/CMSImages/130_Evaluate%20the%20indefinite%20integrals7.png)
Q.9 Sketch the curve and then find the exact arc length of the following curve
y = x2/3
over the interval x = 0 to x = 8.
Q. 10. Derive the following identity:
![2256_Evaluate the indefinite integrals9.png](https://www.expertsmind.com/CMSImages/2256_Evaluate%20the%20indefinite%20integrals9.png)